Search results
Results from the WOW.Com Content Network
In mathematics, a self-adjoint operator on a complex vector space V with inner product , is a linear map A (from V to itself) that is its own adjoint. That is, A x , y = x , A y {\displaystyle \langle Ax,y\rangle =\langle x,Ay\rangle } for all x , y {\displaystyle x,y} ∊ V .
Linear Operators is a three-volume textbook on the theory of linear operators, written by Nelson Dunford and Jacob T. Schwartz. The three volumes are (I) General Theory; (II) Spectral Theory, Self Adjoint Operators in Hilbert Space; and (III) Spectral Operators. The first volume was published in 1958, the second in 1963, and the third in 1971.
The Stone–von Neumann theorem generalizes Stone's theorem to a pair of self-adjoint operators, (,), satisfying the canonical commutation relation, and shows that these are all unitarily equivalent to the position operator and momentum operator on ().
Download QR code; Print/export ... C. Closed linear operator; Compact operator; ... Self-adjoint operator; Semilinear map;
The Helffer–Sjöstrand formula is a mathematical tool used in spectral theory and functional analysis to represent functions of self-adjoint operators.Named after Bernard Helffer and Johannes Sjöstrand, this formula provides a way to calculate functions of operators without requiring the operator to have a simple or explicitly known spectrum.
Download as PDF; Printable version ... von Neumann's theorem is a result in the operator theory of linear operators on Hilbert spaces. Statement of the theorem ...
The set of self-adjoint elements is a real linear subspace of . From the previous property, it follows that A {\displaystyle {\mathcal {A}}} is the direct sum of two real linear subspaces, i.e. A = A s a ⊕ i A s a {\displaystyle {\mathcal {A}}={\mathcal {A}}_{sa}\oplus \mathrm {i} {\mathcal {A}}_{sa}} .
That is, if is a compact self-adjoint operator on , then the essential spectra of and that of + coincide, i.e. () = (+). This explains why it is called the essential spectrum : Weyl (1910) originally defined the essential spectrum of a certain differential operator to be the spectrum independent of boundary conditions.